Question

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates throughout
the year.
The dog's weight W(t) (in kg) as a function of time t (in days) over the course of a year can be modeled by a
sinusoidal expression of the form a.cos(b. t) + d.
Att = 0, the start of the year, he is at his maximum weight of 9.1 kg. One-quarter of the year later, when
t=91.25, he is at his average weight of 8.2 kg.
Find W(t).
t should be in radians.
(2)

Answer 1

Based on the weight and the model that is given, it should be noted that  W(t) in radians will be W(t) = 0.9cos(2πt/366) + 8.2.

How to calculate the radian.

From the information, W(t) = a cos(bt) + d. Firstly, calculate the phase shift, b. At t= 0, the dog is at maximum weight, so the cosine function is also at a maximum. The cosine function is not shifted, so b = 1.

Then calculate d. The dog's average weight is 8.2 kg, so the mid-line d = 8.2. W(t) = a cos t + 8.2. Then calculate a, the dog's maximum weight is 9.1 kg. The deviation from the average is 9.1 kg - 8.2 kg = 0.9 kg. W(t) = 0.9cost  + 8.2

Lastly, calculate t. The period p = 2π/b = 2π/1 = 2π. The conversion factor is 1 da =2π/365 rad. Therefore, the function with t in radians is W(t) = 0.9cos(2πt/365) + 8.2.

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